PROC GLMSELECT: Stepwise Selection(STEPWISE) :: SAS/STAT(R) 9.2 User's Guide, Second Edition

The GLMSELECT Procedure

Stepwise Selection(STEPWISE)

The stepwise method is a modification of the forward selection technique that differs in that effects already in the model do not necessarily stay there.

In the traditional implementation of stepwise selection method, the same entry and removal $\text{[math]}$ statistics for the forward selection and backward elimination methods are used to assess contributions of effects as they are added to or removed from a model. If at a step of the stepwise method, any effect in the model is not significant at the SLSTAY= level, then the least significant of these effects is removed from the model and the algorithm proceeds to the next step. This ensures that no effect can be added to a model while some effect currently in the model is not deemed significant. Only after all necessary deletions have been accomplished can another effect be added to the model. In this case the effect whose addition yields the most significant $\text{[math]}$ value is added to the model and the algorithm proceeds to the next step. The stepwise process ends when none of the effects outside the model has an $\text{[math]}$ statistic significant at the SLENTRY= level and every effect in the model is significant at the SLSTAY= level. In some cases, neither of these two conditions for stopping is met and the sequence of models cycles. In this case, the stepwise method terminates at the end of the second cycle.

Just as with forward selection and backward elimination, you can change the criterion used to assess effect contributions, with the SELECT= option. You can also specify a stopping criterion with the STOP= option and use a CHOOSE= option to provide a criterion used to select among the sequence of models produced. See the discussion in the section Forward Selection (FORWARD) for additional details.

For selection criteria other than significance level, PROC GLMSELECT optionally supports a further modification in the stepwise method. In the standard stepwise method, no effect can enter the model if removing any effect currently in the model would yield an improved value of the selection criterion. In the modification, you can use the DROP=COMPETITIVE option to specify that addition and deletion of effects should be treated competitively. The selection criterion is evaluated for all models obtained by deleting an effect from the current model or by adding an effect to this model. The action that most improves the selection criterion is the action taken.

Examples of Stepwise Selection Specifications

   selection=stepwise

requests stepwise selection based on the SBC criterion. First, if removing any effect yields a model with a lower SBC statistic than the current model, then the effect producing the smallest SBC statistic is removed. When removing any effect increases the SBC statistic, then provided that adding some effect lowers the SBC statistic, the effect producing the model with the lowest SBC is added.

   selection=stepwise(select=SL)

requests the traditional stepwise method. First, if the removal of any effect yields an $\text{[math]}$ statistic that is not significant at the default stay level of 0.15, then the effect whose removal produces the least significant $\text{[math]}$ statistic is removed and the algorithm proceeds to the next step. Otherwise the effect whose addition yields the most significant $\text{[math]}$ statistic is added, provided that it is significant at the default entry level of 0.15.

   selection=stepwise(select=SL stop=SBC)

is the traditional stepwise method, where effects enter and leave based on significance levels, but with the following extra check: If any effect to be added or removed yields a model whose SBC statistic is greater than the SBC statistic of the current model, then the stepwise method terminates at the current model. Note that in this case, the entry and stay significance levels still play a role as they determine whether an effect is deleted from or added to the model. This might result in the selection terminating before a local minimum of the SBC criterion is found.

   selection=stepwise(select=SL SLE=0.1 SLS=0.08 choose=AIC)

selects effects to enter or drop as in the previous example except that the significance level for entry is now $\text{[math]}$ and the significance level to stay is $\text{[math]}$ . From the sequence of models produced, the selected model is chosen to yield the minimum AIC statistic.

   selection=stepwise(select=AICC drop=COMPETITIVE)

requests stepwise selection based on the AICC criterion with steps treated competitively. At any step, evaluate the AICC statistics corresponding to the removal of any effect in the current model or the addition of any effect to the current model. Choose the addition or removal that produced this minimum value, provided that this minimum is lower than the AICC statistic of the current model.

   selection=stepwise(select=SBC drop=COMPETITIVE stop=VALIDATE)

requests stepwise selection based on the SBC criterion with steps treated competitively and where stopping is based on the average square error over the validation data. At any step, SBC statistics corresponding to the removal of any effect from the current model or the addition of any effect to the current model are evaluated. The addition or removal that produces the minimum SBC value is made. The average square error on the validation data for the model with this addition or removal is evaluated. If this average square error is greater than the average square error on the validation data prior to this addition or deletion, then the algorithm terminates at this prior model.

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